Nuclear Instruments and Methods in Physics Research B 127/ 128 ( 19%‘) 225-229

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Monte Carlo simulations of ion-enhanced island coarsening

Eric Chason a* * , Bruce K. Kellerman b

a Sandia National Laboratories, Albuquerque, NM 87185, USA b MEMC Electronic Materials, St. Peters, MO, USA

Abstract Monte Carlo simulations of growth and ion bombardment have been performed to explore the atomistic processes that

occur during ion-assisted growth. The primary elements of the simulation are (1) creation of surface defects (vacancies and adatoms) by ion bombardment and deposition, (2) thermally activated motion of surface defects and (3) recombination of surface vacancies and adatoms. We find that a balance of ion bombardment and deposition (where the creation rate of adatom defects is equal to that of surface vacancies) leads to larger islands and more rapid island coarsening than thermal coarsening with no flux of defects. The presence of the defect flux enhances the breakup of clusters, leading to a broad distribution of island sizes. In comparison, thermal coarsening leads to a more uniform distribution of island sizes that increases in size much more slowly. Histograms of the evolution of the island size distribution provide a quantitative measure of the ion-induced increase in the rate of coarsening.

1. Introduction

Advanced nanostructured materials require well-con- trolled interface and surface morphologies for multiple applications, e.g., in microelectronics, optoelectronics, X- ray optics and magnetic materials. One method that is being studied for controlling morphology during growth is the use of energetic beams in conjunction with deposition to modify surface kinetics and control the growth process. Low energy ion beams have been reported to enhance the smoothness of surfaces during homoepitaxial growth [l] and also to suppress the formation of 3-dimensional is- lands during heteroepitaxy [2,3]. Although these demon- strations of growth enhancement are encouraging, there is not a good understanding of the atomistic mechanisms for ion-assisted growth.

In this work, we report on the results of Monte Carlo simulations of ion-assisted growth in which we explore the atomistic mechanisms that lead to growth enhancement. Using properties of ion-induced and growth-induced de- fects obtained from fundamental studies of surface rough- ening kinetics, we simulate the response of the surface to sequences of growth and ion bombardment to determine if these mechanisms can reproduce the observed roughening and smoothing behavior. In a previous work, we showed how these mechanisms were consistent with measurements of surface smoothing during homoepitaxy [4] on stepped surfaces where the ion-induced defects enhanced the

* Corresponding author. Fax: + l-505-844-1 197; email: ehchaso@sandia.gov

breakup of small islands and the incorporation of atoms into step edges. By promoting growth by step flow rather than nucleation and coalescence of 2-dimensional islands, a smoother surface morphology was achieved, in agree- ment with RHEED measurements.

In this work, we extend this study to look at the kinetics of island coarsening on singular surfaces in the presence of ion- and growth-induced defect fluxes. We show that much larger islands are obtained during ion assisted processing than by purely thermal processes. However, if the number of ion-induced defects is too large then the continuous nucleation of new islands offsets the enhancement in the island size.

2. Simulations

The surface processes considered in the simulations are based on several fundamental studies of low energy ion-in- duced defects using RHEED (Reflection High Energy Electron Diffraction). RHEED is extremely sensitive to small amounts of surface roughness, and by measuring the roughening and smoothing kinetics resulting from different combinations of ion bombardment and growth, several features of ion-assisted growth processes have been deter- mined. The number of surface vacancies and adatoms created per ion has been measured for several species of low energy ions [51. Sequences of growth followed by ion bombardment indicate that the adatoms and surface vacan- cies can recombine, leading to a smoother surface [ 1,6]. Comparison of the temperature-dependent kinetics of sur-

0168-583X/97/$37.00 0 1997 Elsevier Science B.V. All rights reserved. PII SOl68-583X(96)00889-0 II. MODELING/SIMULATION/THEORY

226 E. Chason, B.K. Kellerman/Nucl. Instr. and Meth. in Phys. Res. B 127/ I28 (1997) 225-229

face roughening during ion bombardment with the kinetics of growth roughening indicate that the activation energy for surface vacancy diffusion is comparable to that for adatom diffusion [7]. At elevated temperatures such as those used for ion-assisted growth, recombination of the surface vacancies and adatoms is rapid so that the remain- ing number of defects after recombination is equal to the sputter yield. Previous simulations also indicate that for the ion energies considered, the sputtering process is random and there is no strong preference for sputtering from low coordinated surface sites [8].

The algorithm for implementing these surface processes in a simulation has been described previously [8,9], so it will only be discussed briefly here. The primary steps in the simulation are the creation of defects (surface vacan- cies and adatoms), the thermally activated hopping of the defects on the surface and the annihilation of defects with each other or with existing clusters. We associate a rate with each of these processes, and events are chosen to be performed on the surface based on their relative rates of occurrence.

The activation energy for surface diffusion of isolated adatoms and surface vacancies is taken to be 0.8 eV. An additional 0.2 eV per nearest neighbor is added to the activation energy for hopping of atoms from sites with higher coordination. This extra energy stabilizes clusters and allows nucleation to occur. Vacancy diffusion is im- plemented by considering the coordination of the final site as well as the initial site. If an atom jumps from a 3-fold coordinated site to a O-fold coordinated site, this is a detachment event with an activation energy of 1.4 eV. However, if the atom jumps from a 3-fold coordinated site to another 3-fold coordinated site, this is a vacancy jump and the activation energy is 0.8 eV. There is no additional energy barrier for hopping between levels on the surface and Cfold coordinated atoms in the surface are not al- lowed to move. Annihilation occurs whenever defects of opposite sign occupy the same site by random jumps. There is no attractive interaction between defects of oppo- site sign. The initial surface is a flat array of 256 X 256 atoms and the simulation temperature is 200°C. The calcu- lations were performed on an HP Vectra computer with a 133 MHz Pentium processor. Typical simulation runs re- quired 6-24 h to complete. To obtain sufficient statistics for the island size distributions, 4-6 simulation runs under the same conditions were added together.

All the simulations discussed here start with 0.25 monolayers (ML) of deposition at a deposition rate of 0.1 ML/s. After the initial deposition, three different condi- tions were studied: (1) terminate growth flux, allow ther- mal coarsening to occur, (2) continue growth flux, turn on equal ion flux (each ion creates one vacancy defect), (3) continue growth flux, turn on equal ion flux (each ion creates 9 defects: 5 vacancies and 4 adatoms). The spatial distribution of the 9 defects was determined from simula- tions of ion-induced bulk defect creation and diffusion to

the surface based on TRIM simulations [4]. In all cases, after the initial growth sequence the net defect creation rate (vacancies minus adatoms) is equal to zero so that on average no material is being added to or removed from the surface. However, the total defect creation rate varies from zero (thermal coarsening) to 10 ML/s.

3. Results and discussion

The surface morphology at different stages of the simu- lation are shown in Fig. 1. Fig. la shows the surface after 0.25 ML of growth, which is the typical surface morphol- ogy before coarsening. The other panels show the surfaces after subsequent 77.5 s of annealing under the following conditions: lb thermal annealing (no growth or ion flux); lc ion bombardment and growth with 1 vacancy defect per ion and Id ion bombardment and growth with 9 defects created per ion. The island sizes in the thermal case appear to be much more regular than for the ion assisted cases. The largest islands are found for the case of ion-assisted coarsening with 1 vacancy/ion (Fig. lc), although there are also many small clusters present. The case of 9 de- fects/ion (Fig. Id) also has some large clusters, but now there is a very large number of small clusters of adatoms and vacancies.

More quantitative understanding can be obtained by looking at the evolution of the island sizes for the different coarsening conditions (shown in Fig. 2). The data are presented as the island size, n, versus the fractional cover- age of the surface by islands of size n (equal to the number of islands of size n multiplied by the size of the island and normalized by the area of the surface). In this way, the distribution (called the island coverage distribution) is weighted so that its magnitude reflects the fraction of the surface covered by islands of size n. Shown in Fig. 2 are the island coverage distributions obtained after 17.5, 37.5 and 77.5 s of processing after growth for the cases of thermal coarsening (a-c), one vacancy per ion (d-f) and 9 defects/ion (g-i). The mean of the distribution is indi- cated by the vertical dashed line. The evolution of the mean of the island coverage distribution with time for each of the simulation conditions is shown in Fig. 3.

For the case of thermal coarsening, the mean of the island coverage distribution increases slowly with time. The distribution also stays quite sharp, as indicated by the relatively uniform size of the islands seen in Fig. lb. The addition of deposition and ion-induced defects signifi- cantly changes the shape of the island coverage distribu- tions and the evolution of the mean. For the case of 1 vacancy/ion, the mean of the distribution increases much more quickly than the thermal case so that at the end of the simulation the mean size is 318 atoms as compared with 140 for thermal coarsening. The island coverage distribu- tion is also much broader, encompassing very large islands as well as many small clusters. Increasing the number of

E. Chuson. B.K. Kellerman / Nucl. Instr. and Meth. in Phys. Res. B 127 / 128 (1997) 225-229 221

Fig. 1. Surfaces produced by computer simulation of growth and ion bombardment. Lighter shades represent higher spots on the surface. (a) After initial growth of 0.25 ML before coarsening, (b) after 77.5 s of thermal coarsening (no growth and no ion flux), (c) after 77.5 s of ion assisted coarsening, 1 vacancy per ion, ion flux equal to growth flux, (d) after 77.5 s of ion assisted coarsening, 9 defects (5 vacancies and 4 adatoms) per ion, ion flux equal to growth flux.

0.09

!io.U2 m’S ‘sol

P- r: 0.00

0 200 400 600 3on

(d) 17.5 s 1 vacancylion

0 200 400 WJ 800

i I (e) 37.5 s 1 vacancy/ion

island size, n island size. n

0 2cJa 400 600 80 0

0 200 400 6008w Island size, n

Fig. 2. Island size, n, versus fraction of surface covered by islands of size n: (a)-(c) thermal coarsenmg, (no growth and no ion flux); (d)-(f) ion assisted coarsening, 1 vacancy per ion, ion flux equal to growth flux; (g)-(i) ion assisted coarsening, 9 defects (5 vacancies and 4 adatoms) per ion, ion flux equal to growth flux. Length of simulated time after initial growth sequence indicated in figure.

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w *z A thermal 300 - 000 -0 0 O 5 1 vacancy/ion o o 0 - +

z 9 defects/ion o

s 200- oo”

“E 0 0 ++

P 0 +++

++++++++

E,oo_ o+A~~Ah AAA

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.p 2kA

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01 0 20 40 60 80

coarsening time

Fig. 3. Evolution of mean of island coveragee distributions for thermal coarsening and ion assisted coarsening with 1 vacancy/ion and 9 defects/ion.

defects created per ion from 1 to 9 leads to a very broad distribution that is peaked at small island size. Although the largest islands formed are significantly larger than for the thermal case (with clusters as large as 775 atoms present), the presence of many small clusters makes the mean of the distribution only slightly larger than for the thermal case.

The results for the thermal coarsening case are consis- tent with the classical picture of island ripening [lo] in which the greater equilibrium “vapor pressure” of adatoms around small islands leads them to decay more rapidly than large islands. This process is mediated by adatoms that detach from the island edges by thermally-activated hops. The sharpness of the distributions shown in Fig. 2a-c means that there is not a large variation in the island sizes present. Consequently, the driving force for the large islands to grow at the expense of the smaller ones is relatively small, and the mean island size increases slowly as shown in Fig. 3.

The addition of deposition and ion bombardment greatly increases the concentration of defects on the surface rela- tive to the number that are created thermally. The supersat- uration is high enough to lead to nucleation of new clusters on the surface, which shows up as an increase in the coverage of small clusters in the cluster size distributions for 1 vacancy/ion (Fig. 2d-f) and 9 defects/ion (Fig. 2f-i). The nucleation of new clusters is not considered in the classical picture of ripening which assumes a low defect concentration. However, the addition of additional defects alone does not lead to enhanced coarsening. There must be a size-dependent effect that leads to more rapid decay of small islands relative to large islands.

One possible explanation is to look at the effects of surface vacancies on the detachment of atoms from is- lands. Detachment from islands occurs at l-, 2- and ~-CO-

ordinated sites with correspondingly higher activation en- ergies as described in Section 2. The island shapes after growth (Fig. la) and after thermal coarsening (Fig. lb) are relatively compact, so that there are a large number of

3toordinated sites on the perimeter of the island. In the presence of ion-induced defects, however, the annihilation of surface vacancies with atoms on the edges of clusters leads to the production of many more a-coordinated sites (kink sites) from which detachment can occur more rapidly. Changing a 3-coordinated site to a 2-coordinated kink site has a greater effect on the decay of small clusters than large clusters because of the fewer number of atoms on the island edge. This explanation is consistent with the more irregular island morphologies produced by ion-assisted coarsening as seen in Fig. lc, d. In this picture, the ion-induced defects enhance coarsening by changing the number of available sites for detachment. This suggests that changing the rate of diffusion around the island edge (relative to the rate of defect production) may have a strong influence on the ion-assisted coarsening by modify- ing the island shape, but this has not yet been tested.

It is important to recognize that the results discussed above do not consider the effects of changing temperature, defect fluxes and activation energies. The addition of athermal defects will not necessarily lead to an increase in the coarsening under all conditions. The observed effect of ion-enhanced coarsening is caused by changing the bal- ance between multiple surface processes so that the breakup of islands is enhanced without introducing too many new clusters. However, with different values of the simulation parameters the increase in the coarsening rate may not be as significant. For instance, at higher temperatures the detachment rates of atoms from islands may be sufficiently high that the addition of athermal defects would not sub- stantially change the coarsening rate. The significance of these results is that the addition of athermal defects pro- vide an atomistic mechanism that can lead to an increase in coarsening. Further simulation studies and the develop- ment of an analytical theory for ion-assisted coarsening are needed to determine under what range of conditions the increase in coarsening occurs.

4. Summary

We have used Monte Carlo simulations to study the effect of ion-induced defects on the evolution of 2-dimen- sional island size distributions. A significant increase in the mean island size is observed during simultaneous deposition and ion bombardment when the growth flux is equal to the ion flux and each ion creates one surface vacancy defect. These results indicate that a simple mecha- nism of independently diffusing surface vacancies and adatoms can lead to more rapid development of large 2-dimensional islands than by thermal annealing alone. Creation of multiple defects per ion, however, leads to continuous nucleation of new clusters which offsets the increased coarsening of the islands.

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Admowledgements

We gratefully acknowledge useful discussions and sup- port from John Hunter, Jerry Floro, Tom Mayer and Roland Stumpf. This work was performed at Sandia Na- tional Laboratories and supported by the U.S. Department of Energy under contract DE-ACO4-94AL85000.

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